tailieunhanh - Kinetics of Materials - R. Balluff_ S. Allen_ W. Carter (Wiley_ 2005) Episode 11

Tham khảo tài liệu 'kinetics of materials - r. balluff_ s. allen_ w. carter (wiley_ 2005) episode 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 436 CHAPTER 18 SPINODAL AND ORDER-DISORDER TRANSFORMATIONS order parameters such as for A2 B2 7eq 0 77 77eq there is no bias to form one ordered B2 variant over another the two equivalent variants are indicated by B2 see Fig. . The two equivalent variants emerge at random locations and interfaces develop as one impinges upon the other. For conserved order parameters such as composition interfaces between phases on phase-diagram tie-lines necessarily appear. In the absence of interfaces a linear kinetic theory could be developed where the transformation driving force derives from decreases in homogeneous molar free energy as derived in Eqs. and for the conserved and nonconserved cases. However at the onset of a continuous phase transition the system is virtually all interface between new phases or variants. For example when equivalent variants emerge in adjacent regions during ordering gradients in the order parameter are generated these constitute emerging diffuse antiphase boundaries. Neglecting the contribution of these interfaces leads to ill-posed linearized kinetics as indicated by the negative interdiffusivity in Eq. . The theory for the free energy of inhomogeneous systems incorporates contributions from interfacial free energy through the diffuse interface method 3 . Interfaces are defined by the locations where order parameters change and can be located by the regions with significant order-parameter gradients. Interfacial energy appears in the diffuse-interface methods because order-parameter gradients contribute extra energy. Free Energy of an Inhomogeneous System Let ffr represent either a conserved or a nonconserved order parameter such as cb F or 77 F . Also let the field f f F V F be the free-energy density energy volume at position r. The homogeneous free-energy density hom C V 0 is the free-energy density in the absence of gradients and is related to molar free energies F IVo i2 hom C used to construct phase diagrams .